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%I #9 Dec 28 2022 09:04:58
%S 1,2,1,1,1,3,2,2,4,2,1,1,1,2,1,3,3,3,5,2,2,2,1,6,1,1,4,4,3,2,1,1,1,1,
%T 4,7,2,2,2,1,8,5,3,3,3,4,3,5,5,2,2,9,2,2,2,2,1,3,1,6,6,6,2,1,1,3,4,4,
%U 4,7,10,3,3,2,11,3,3,1,1,1,1,1,4,5,4
%N Triangle read by rows: if n has weakly increasing prime indices (a,b,...,y,z) then row n is (z-a+1, z-b+1, ..., z-y+1).
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e Triangle begins:
%e 1: .
%e 2: .
%e 3: .
%e 4: 1
%e 5: .
%e 6: 2
%e 7: .
%e 8: 1 1
%e 9: 1
%e 10: 3
%e 11: .
%e 12: 2 2
%e 13: .
%e 14: 4
%e 15: 2
%e 16: 1 1 1
%e 17: .
%e 18: 2 1
%e 19: .
%e 20: 3 3
%e For example, the prime indices of 900 are (1,1,2,2,3,3), so row 900 is 3 - (1,1,2,2,3) + 1 = (3,3,2,2,1).
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[If[n==1,{},1+Last[primeMS[n]]-Most[primeMS[n]]],{n,100}]
%Y Row lengths are A001222(n) - 1.
%Y Indices of empty rows are A008578.
%Y Even-indexed rows have sums A243503.
%Y Row sums are A326844(n) + A001222(n) - 1.
%Y An opposite version is A356958, Heinz numbers A246277.
%Y Heinz numbers of the rows are A358195, even bisection A241916.
%Y A112798 list prime indices, sum A056239.
%Y A243055 subtracts the least prime index from the greatest.
%Y Cf. A055396, A124010, A253565, A325351, A325352, A355534, A355536, A358137.
%K nonn,tabf
%O 1,2
%A _Gus Wiseman_, Dec 20 2022
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